Determine if the two vectors u = - 3i - j and v = 2i + 2j are orthogonal. If they are not orthogonal, specify the angle between them

Two vectors by definition are orthogonal when the angle between them is 90 degrees.

It can also be said that they are orthogonal if the scalar product between both vectors is zero.

We have then:

u = - 3i - j

v = 2i + 2j

u. v = ( - 3i - j) (2i + 2j) = - 6-2

u. v = - 8

They are not orthogonal vectors.

The angle between them is

lul = root (( - 3) ^ 2 + (-1) ^ 2) = 3.16227766

lvl = root ((2) ^ 2 + (2) ^ 2) = 2.828427125

The angle between them is:

cos (x) = (u. v) / ((lul) * (lvl))

cos (x) = ( - 8) / ((3.16227766) * (2.828427125))

cos (x) = - 0.894427191

x = acos (-0.894427191)

x = 153.4349488

x = 153.43

Answer:

It is not orthogonal

Angle between them:

x = 153.43